Hamiltonian dynamics Properties of Hamiltonian Dynamics - Reversibility The mapping Is determined by Hamiltonian's equation from(a(t),p(t) to( q(t +s),p(t +s)) is one to one The inverse mapping is just negate p and apply Ts( See the Hamilton's equation Conservation of the hamiltonian The system evolves with its hamiltonian unchanged dh d ∑ dq: ah dp; aH ∑ ah ahaHaH 0 i=1 api agi aqi apiHamiltonian Dynamics • Properties of Hamiltonian Dynamics – Reversibility • The mapping 𝑇𝑠 determined by Hamiltonian’s equation from 𝑞 𝑡 ,𝑝 𝑡 to 𝑞 𝑡 + 𝑠 ,𝑝 𝑡 + 𝑠 is one to one. The inverse mapping is just negate 𝑝 and apply 𝑇𝑠 . (See the Hamilton’s equation.) – Conservation of the Hamiltonian • The system evolves with its Hamiltonian unchanged: